I have some questions about two statements from Bosch's "Algebraic Geometry and Commutative Algebra" about algebraic varieties (page 479):
W fix an abelian variety $A$ over field $K$. Here the definition
Following two questions:
Why is for a $K$-group scheme of finite type smooth equivalent to geometrically reduced?
Why under same conditions as in 1. (so $K$-group scheme of finite type) the property irreducible is equivlaent to geometrically irreducible?